🔬 materials science

AI-enhanced discovery and accelerated synthesis of metal phosphosulfides

This paper presents an integrated workflow combining density functional theory, multi-fidelity machine learning, and high-throughput combinatorial synthesis to successfully discover and rapidly synthesize previously unknown metal phosphosulfides, demonstrating that accelerated materials development is viable even for challenging inorganic systems.

Original authors: Javier Sanz Rodrigo, Nicholas A. Kryger-Nelson, Lena A. Mittmann, Eugène Bertin, Ivano E. Castelli, Andrea Crovetto

Published 2026-01-26

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CC BY 4.0

Original authors: Javier Sanz Rodrigo, Nicholas A. Kryger-Nelson, Lena A. Mittmann, Eugène Bertin, Ivano E. Castelli, Andrea Crovetto

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a chef trying to invent a new type of soup. You have a pantry full of ingredients: metals, phosphorus, and sulfur. In the world of chemistry, mixing these three creates a family of materials called metal phosphosulfides. These materials are like "super-ingredients" that can conduct electricity, store energy, or interact with light in special ways.

However, making these soups is notoriously difficult. Unlike common ingredients like salt or sugar (which are like oxides and nitrides in chemistry), phosphorus and sulfur are volatile, corrosive, and tricky to handle. For a long time, scientists have been making these materials one pot at a time, slowly testing recipes one by one. This is like trying to find the perfect soup flavor by tasting a single spoonful every day for years.

This paper describes a new, faster way to cook: AI-enhanced discovery and accelerated synthesis. Here is how they did it, broken down into simple steps:

1. The Digital Taste-Test (AI & Theory)

Before cooking anything in the real world, the team used a supercomputer to simulate thousands of potential recipes.

The Menu: They looked at 909 different possible combinations of metals, phosphorus, and sulfur.
The Filter: They used a digital tool called "Density Functional Theory" (think of it as a high-tech taste-tester) to see which recipes were stable enough to exist and which would fall apart.
The Discovery: Out of all those possibilities, they found 19 new, stable recipes that no one had ever made before, including some based on Silicon and Germanium.
The Prediction: They also needed to know how much energy these materials could block or pass (called a "band gap"). Since running a super-accurate simulation for every single recipe would take too long, they built a Machine Learning model. Think of this as a "smart translator." It took quick, rough estimates from the computer and translated them into highly accurate predictions of what the real-world energy levels would be.

2. The "Magic Pan" (High-Throughput Synthesis)

Once the AI gave them a shortlist of promising recipes, they needed to make them. But they didn't want to make them one by one.

The Problem: Traditional methods are slow and serial (one after another).
The Solution: They used a special technique called DADMARS. Imagine a giant frying pan where you can spray different amounts of ingredients across the surface at the same time.
The Result: In a single experiment, they created a "combinatorial library" containing over 100 different compositions on a single thin film (like a microscopic pizza with 100 different toppings).
The Efficiency: Using this method, they successfully synthesized four distinct new materials in just four experiments. They didn't need a pre-written recipe; the AI told them what to look for, and the magic pan made it happen instantly.

3. The Taste-Test Results (Characterization)

After making the films, they checked to see if the AI was right.

Stability: They confirmed that the materials they made were indeed stable and matched the computer predictions.
Band Gaps: They measured how these materials interact with light. The AI's "translator" model was incredibly accurate, predicting the energy levels with very little error compared to the actual lab measurements.
The "Flavor" Profile: They discovered that these materials come in two main "flavors":
1. Thiophosphates: Where phosphorus acts like a positive ingredient bonded to sulfur. These tend to be good semiconductors (useful for electronics).
2. Non-Thiophosphates: Where phosphorus acts differently, sometimes bonding directly to metals. These can be metals or have very different electronic properties.

The Big Picture

The main takeaway is that AI and high-speed experiments can work together to solve difficult chemistry problems. Even for materials that are hard to make (like those with phosphorus and sulfur), you don't have to guess and check for decades.

By combining:

Theory (The computer menu),
AI (The smart translator), and
High-Throughput Synthesis (The magic pan that makes 100 soups at once),

The team proved that we can rapidly discover and create new materials that were previously too difficult to find. They didn't just find one new material; they built a system that can find any new material in this family, opening the door to a much wider variety of future technologies.

Problem Statement
Metal phosphosulfides represent a versatile class of multifunctional materials with potential applications in solid-state batteries, ferroelectrics, and nonlinear optics. However, their development has been hindered by significant synthesis challenges compared to established material classes like oxides and nitrides. Historically, research has proceeded in "material silos," focusing on individual compounds or specific application-driven searches rather than broad, accelerated exploration. Furthermore, existing synthesis procedures are typically serial and low-throughput, lacking the ability to screen compositional and process parameters in parallel. This has resulted in a limited theoretical understanding of synthesizability and band gaps across the broader phosphosulfide landscape.

Methodology
The authors employed a combined workflow integrating high-throughput density functional theory (DFT), multi-fidelity machine learning (ML), and experimental high-throughput synthesis:

Computational Screening: The team calculated the thermodynamic stability and band gaps of 909 hypothetical ternary metal phosphosulfides using DFT (specifically the PBEsol functional). They constructed convex hulls to determine energy above the hull ( $E_h$ ) and defined a stability tolerance of 0–100 meV/atom.
Machine Learning Model: To address the computational cost of high-accuracy band gap calculations, a multi-fidelity deep learning model based on permutation-invariant transformers was developed. This model translates semilocal PBEsol band gaps into experimentally calibrated band gaps using elemental composition and PBEsol values as inputs. The model was trained on datasets from the Materials Project, SNUMAT, and experimental compilations.
Experimental Validation: The authors utilized a high-throughput thin-film combinatorial synthesis technique called Directional-and-Diffuse Multi-Anion Reactive Sputtering (DADMARS). This method allows for the deposition of films with intentional elemental composition gradients across a single substrate. Four combinatorial experiments were conducted on the Cu-P-S and Ag-P-S systems to synthesize and characterize materials without prior synthesis recipes.

Key Results

Thermodynamic Stability and New Compounds: The screening identified 19 previously unknown ternary phosphosulfides predicted to be thermodynamically stable ( $E_h = 0$ ), including the first Si- and Ge-based phosphosulfides (SiP $_2$ S $_6$ and GePS $_3$ ). Additionally, 71 metastable compositions with $E_h < 50$ meV/atom were identified. The study found that synthesizability is highly correlated with $E_h$ ; while 60% of materials on the stability hull have been synthesized, this rate drops to 3% for materials with $50 < E_h < 100$ meV/atom.
Structural Classification: The study classifies phosphosulfides into two distinct categories based on the P/S ratio:
- Thiophosphates (P/S $\le$ 1/3): Phosphorus is in a positive oxidation state (+4 or +5) and forms polyanionic motifs (e.g., isolated [PS $_4$ ] $^{3-}$ , corner-sharing, edge-sharing, or ethane-like structures) without bonding directly to the metal cation. These are predominantly charge-balanced semiconductors.
- Non-Thiophosphates (P/S > 1/3): Phosphorus adopts negative or neutral oxidation states and bonds directly to the metal. These include motifs like P-S units, S-P-P-S chains, and phosphorus nets. This class exhibits a more complex distribution of electronic properties, including metallic behavior and narrow band gaps.
Band Gap Prediction: The multi-fidelity ML model achieved a mean absolute error (MAE) of 0.24 eV when predicting experimental band gaps from PBEsol inputs, outperforming simple polynomial fitting between PBEsol and HSE functionals (MAE 0.41 eV). The model revealed that thiophosphates generally possess band gaps in the 2.3–3.0 eV range, while non-thiophosphates show a broader distribution including metallic states and lower gaps.
Experimental Synthesis: Using only four combinatorial experiments, the team successfully synthesized four distinct single-phase thin-film compounds: Cu $_3$ PS $_4$ , Cu $_7$ PS $_6$ , Ag $_3$ PS $_4$ , and Ag $_7$ PS $_6$ . Notably, Ag $_3$ PS $_4$ and Ag $_7$ PS $_6$ were obtained in a single run. The synthesized films were air-stable semiconductors with band gaps in the visible range, confirming the viability of the high-throughput approach for "difficult" chemistries.

Significance and Claims
The paper argues that accelerated materials development workflows, which integrate theory, artificial intelligence, synthesis, and characterization, are viable even for experimentally challenging inorganic materials like phosphosulfides. The authors demonstrate that:

Broad computational screening can identify stable, unexplored compositions (including Si/Ge-based systems) that were previously unknown.
Multi-fidelity machine learning can effectively bridge the gap between fast, low-accuracy DFT calculations and experimental reality for band gap prediction.
High-throughput experimental methods (specifically DADMARS) can overcome the traditional barriers of synthesizing phosphosulfides, enabling the rapid discovery of new thin-film materials without requiring prior synthesis recipes.

The work concludes that the "difficult" nature of phosphorus and sulfur chemistry does not preclude accelerated discovery, provided that suitable high-throughput experimental setups are implemented. The findings provide a foundational map of the structural, compositional, and electronic diversity of metal phosphosulfides, offering a basis for future intelligent searches for novel materials with new compositions and higher complexity.

1. The Digital Taste-Test (AI & Theory)

2. The "Magic Pan" (High-Throughput Synthesis)

3. The Taste-Test Results (Characterization)

The Big Picture

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